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Construct the truth table of the following: [(∼p ∨ q) ∧ (q → r)] → (p → r) - Mathematics and Statistics

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प्रश्न

Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)

योग

उत्तर

p q r ∼p ∼p ∨ q q→r (∼p∨q) ∧ (q→r) p→r [(∼p∨q) ∧ (q→r)] → (p→r)
T T T F T T T T T
T T F F T F F F T
T F T F F T F T T
T F F F F T F F T
F T T T T T T T T
F T F T T F F T T
F F T T T T T T T
F F F T T T T T T
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अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 6.5 | पृष्ठ ३३

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q


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(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls


Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu.


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


If p ∧ q is false and p ∨ q is true, then ______ is not true.


Construct the truth table of the following:

p → (q → p)


Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]


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(p ∨ q) is T and (p ∨ q) → q is F


Determine the truth values of p and q in the following case:

(p ∧ q) is F and (p ∧ q) → q is T


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Express the following statement in symbolic form.

Milk is white or grass is green.


Express the following statement in symbolic form.

I like playing but not singing.


Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.


Write the truth value of the following statement.

The Himalayas are the highest mountains but they are part of India in the North East.


Write the negation of the following statement.

− 3 is a natural number.


Write the negation of the following statement.

It is false that Nagpur is capital of Maharashtra


Write the negation of the following statement.

2 + 3 ≠ 5


Write the truth value of the negation of the following statement.

`sqrt5` is an irrational number.


Write the truth value of the negation of the following statement.

London is in England.


Write the following statement in symbolic form.

If triangle is equilateral then it is equiangular.


Write the following statement in symbolic form.

Even though it is not cloudy, it is still raining.


Write the following statement in symbolic form.

Milk is white if and only if the sky is not blue.


Write the following statement in symbolic form.

Stock prices are high if and only if stocks are rising.


Find the truth value of the following statement.

It is not true that 3 − 7i is a real number.


Find the truth value of the following statement.

If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.


Find the truth value of the following statement.

Every accountant is free to apply his own accounting rules if and only if machinery is an asset.


If p and q are true and r and s are false, find the truth value of the following compound statement.

p ∧ (q ∧ r)


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ∨ (r ∧ s) 


If p and q are true and r and s are false, find the truth value of the following compound statement.

~ [(~ p ∨ s) ∧ (~ q ∧ r)]


If p and q are true and r and s are false, find the truth value of the following compound statement.

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]


Assuming that the following statement is true,

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q : Ram does not study on holiday,

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Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

If Sunday is not holiday then Ram studies on holiday.


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is a holiday and Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)


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q : Water is warm

Give the verbal statement for the following symbolic statement.

q → p


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q : Water is warm

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q ∧ ~ p


Fill in the blanks :

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Assuming the first statement p and second as q. Write the following statement in symbolic form.

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Assuming the first statement p and second as q. Write the following statement in symbolic form.

To be brave is necessary and sufficient condition to climb the Mount Everest.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

The drug is effective though it has side effects.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

If a real number is not rational, then it must be irrational.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

It is not true that intelligent persons are neither polite nor helpful.


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If proof is lengthy then it is interesting.


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q : Sachin is a member of Rajya Sabha.
r :
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r : Sachin is happy.
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r : Sachin is happy.
Write the verbal statement of the following.

∼ (p ∨ q) ∧ r


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An angle is a right angle if and only if it is of measure 90°.


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4 is an odd number if 3 is not a prime factor of 6.


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


If p, q are true statements and r, s are false statements, then write the truth value of the compound statement

(p `→` ∼ r) `→` (q ∧ s)


Write the negation of (p `leftrightarrow` q).


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


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